We consider a uniaxial and biaxial ferromagnetic nanowire with a head-to-head DW at the centre along the \(x\) -axis (easy axis) of length \(L_x\)  and cross-sectional area \(L_y \times L_z\)  as shown in Fig.REF . The DW width \(\Delta \)  is larger than the dimension of \(L_y\) , \(L_z\)  but much smaller than \(L_x\) . The hard anisotropy of biaxial nanowire is given by \(K_{\perp }=1/2 \mu _oM^2_s(\mathcal {N}_y-\mathcal {N}_z)\)  along \(z\) -direction with \(\mathcal {N}_z \ge \mathcal {N}_y\) , where \(\mathcal {N}_x,\mathcal {N}_y\)  and \(\mathcal {N}_z\)  are demagnetization factors. However, for uniaxial nanowire, \(\mathcal {N}_z = \mathcal {N}_y\) , i.e., \(K_\perp = 0\) . A TG as a driving force is applied along the nanowire. The applied highest temperature is far below the Curie temperature \(T_{c}\) . It is assumed that the saturation magnetization and exchange constant are temperature-independent. The magnetization dynamics is governed by the stochastic Landau-Lifshitz-Gilbert (sLLG) equation [1]}, [2]},
\(\dfrac{d\textbf {m}}{dt}=-\textbf {m}\times (\textbf {h}_{\text{eff}}+ \textbf {h}_{\text{th}})+\alpha \textbf {m}\times \dfrac{\partial \textbf {m}}{\partial {t}},\) 
